Showing 1 to 27 of 27

Exam 1
October 5, 2010
Joel M. Cohen
Name:
Math 432
11:00-12:15
1. (35 points) Let R2 be the plane with the standard topology and X the plane
with the dictionary ordering topology.
(a) Prove that the latter topology is strictly bigger than the standard to

Exam 1
October 5, 2010
Joel M. Cohen
Name:
Math 432
11:00-12:15
1. (35 points) Let R2 be the plane with the standard topology and X the plane
with the dictionary ordering topology.
(a) Prove that the latter topology is strictly bigger than the standard to

Exam 1
October 12, 2006
Joel M. Cohen
Name:
Math 432
3:30-4:45 p.m.
1. (35 points) Let R be the real numbers with the standard topology and X the
real numbers with the nite complement topology. Since the latter has many fewer
open sets, given a function f

Exam 2
December 7, 2006
Joel M. Cohen
Name:
Math 432
3:30-4:45 p.m.
1. (20 points) Let R be given the nite complement topology (the closed sets are
R and nite sets). Prove that every subset is compact.
2. (20 points) Show that no two of R1 , R2 and R3 are

Exam 2
December 7, 2006
Joel M. Cohen
Name:
Math 432
3:30-4:45 p.m.
1. (20 points) Let R be given the nite complement topology (the closed sets are
R and nite sets). Prove that every subset is compact.
2. (20 points) Show that no two of R1 , R2 and R3 are

Exam 1
October 12, 2006
Joel M. Cohen
Name:
Math 432
3:30-4:45 p.m.
1. (35 points) Let R be the real numbers with the standard topology and X the
real numbers with the nite complement topology. Since the latter has many fewer
open sets, given a function f

Exam 1
October 5, 2010
Joel M. Cohen
Name:
Math 432
11:00-12:15
1. (35 points) Let R2 be the plane with the standard topology and X the plane
with the dictionary ordering topology.
(a) Prove that the latter topology is strictly bigger than the standard to

Exam 1
October 12, 2006
Joel M. Cohen
Name:
Math 432
3:30-4:45 p.m.
1. (35 points) Let R be the real numbers with the standard topology and X the
real numbers with the nite complement topology. Since the latter has many fewer
open sets, given a function f

Exam 2
December 7, 2006
Joel M. Cohen
Name:
Math 432
3:30-4:45 p.m.
1. (20 points) Let R be given the nite complement topology (the closed sets are
R and nite sets). Prove that every subset is compact.
2. (20 points) Show that no two of R1 , R2 and R3 are